### Abstract

We prove all the maximizers of the sharp Hardy-Littlewood-Sobolev inequality are smooth. More generally, we show all the nonnegative critical functions are smooth, radial with respect to some points and strictly decreasing in the radial direction. In particular, we resolve all the cases left open by previous works of Chen, Li and Ou on the corresponding integral systems.

Original language | English (US) |
---|---|

Pages (from-to) | 373-383 |

Number of pages | 11 |

Journal | Mathematical Research Letters |

Volume | 14 |

Issue number | 2-3 |

State | Published - Mar 2007 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Research Letters*,

*14*(2-3), 373-383.

**On the integral systems related to Hardy-Littlewood-Sobolev inequality.** / Hang, Fengbo.

Research output: Contribution to journal › Article

*Mathematical Research Letters*, vol. 14, no. 2-3, pp. 373-383.

}

TY - JOUR

T1 - On the integral systems related to Hardy-Littlewood-Sobolev inequality

AU - Hang, Fengbo

PY - 2007/3

Y1 - 2007/3

N2 - We prove all the maximizers of the sharp Hardy-Littlewood-Sobolev inequality are smooth. More generally, we show all the nonnegative critical functions are smooth, radial with respect to some points and strictly decreasing in the radial direction. In particular, we resolve all the cases left open by previous works of Chen, Li and Ou on the corresponding integral systems.

AB - We prove all the maximizers of the sharp Hardy-Littlewood-Sobolev inequality are smooth. More generally, we show all the nonnegative critical functions are smooth, radial with respect to some points and strictly decreasing in the radial direction. In particular, we resolve all the cases left open by previous works of Chen, Li and Ou on the corresponding integral systems.

UR - http://www.scopus.com/inward/record.url?scp=34547408245&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547408245&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34547408245

VL - 14

SP - 373

EP - 383

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 2-3

ER -